Reserving S40 from 15K-25K (recommended base, 558 k's).
I'm not sure if I'll actually want to finish it all the way to 25K, but I'm sieving it now. I'll at least sieve it to 30G, which I estimate to be my optimal depth. So at minimum, there'll be a sieve file for it.

[QUOTE=Mini-Geek;235800]Reserving S40 from 15K-25K (recommended base, 558 k's).
I'm not sure if I'll actually want to finish it all the way to 25K, but I'm sieving it now. I'll at least sieve it to 30G, which I estimate to be my optimal depth. So at minimum, there'll be a sieve file for it.[/QUOTE]

This might take you less time than you expect. The tests are fairly quick. You will probably complete the range on a single core in less than two months.

[QUOTE=rogue;235811]This might take you less time than you expect. The tests are fairly quick. You will probably complete the range on a single core in less than two months.[/QUOTE]

Was that a guess or have you calculated this? I just calculated, and got a surprisingly close figure to yours: at the current sieve depth (1G; I have ~15.5k more factors up to 3.6G, but they haven't been eliminated yet. I expect to find ~22904 more factors up to 30G) and ignoring that k's will be removed due to primes, I estimate 67 core days to complete the range. Factor those two things in, and it's easily under 2 months, maybe closer to 1.5. Anyway, I should be done with this within a couple weeks, so I don't see a problem in doing it. :smile:
Edit: Oops, I counted the number of factors from an even lower sieve depth, 1M. So it's actually a good deal shorter than this. 264013 terms remain at 1G, 395964 did at 1M. New rough estimate for 1G and ignoring removing k's is 44.7 days. Looks like 1 core month is really a better estimate, and your estimate is a bit pessimistic.
Estimating for 30G with 4 cores and removing primes...I guess it'll take a bit over a week (6-9 days) once sieving is done (which is itself about 4*8 CPU hours).

S49 complete to 100K, releasing. 3 primes total, already reported:
2746*49^49438+1
2694*49^60523+1
1134*49^66183+1
Results attached, I used the posted sieve file.

[QUOTE=Mini-Geek;235913]S49 complete to 100K, releasing. 3 primes total, already reported:
2746*49^49438+1
2694*49^60523+1
1134*49^66183+1
Results attached, I used the posted sieve file.[/QUOTE]

Outstanding! Base 49 is truly a "prime" base. The Riesel side has one k remaining at n=200K for CK=2414 and the Sierp side has two k's remaining at n=100K for CK=2944. Both give us a good chance to break the CRUS proven CK record set by S36 at CK=1886.

[QUOTE=gd_barnes;236043]Outstanding! Base 49 is truly a "prime" base. The Riesel side has one k remaining at n=200K for CK=2414 and the Sierp side has two k's remaining at n=100K for CK=2944. Both give us a good chance to break the CRUS proven CK record set by S36 at CK=1886.[/QUOTE]

I'm not so optimistic: these two k's were the lowest weight out of the five, by far. Searching n=100K-400K for both Sierp k's gives an expected 0.44 primes, or 35.6% chance of at least one prime. The per-doubling expected primes (this can be compared to the Riesel side's 200-400, which is a doubling) is 0.22, or 19.9%. It's a bit less if you stop searching a k once a prime is found for it. Searching 200K-400K for the one Riesel k is 0.19 expected primes, with a 17.2% chance of finding a prime. Except for the current depth difference, the Riesel side looks far better to me, because it's almost as high of a weight as the other two combined, (Riesel's 1 k is 0.19 primes per doubling, Sierp's 2 k's are 0.22 primes per doubling; an equivalent comparison is the number of candidates in 200K-400K after sieving to 1M: Riesel is 8640, Sierp is 10002, i.e. Sierp is about 15.8% more candidates) and you only need one prime. n=400K on either base is about the same size as 10^676078 or 2^2245883. That represents a significant amount of work.
It may be true that both have been extremely 'prime' so far, but I don't think there's any reason that will continue, so we're just left with the expected primes from the weights, which are, unfortunately, rather bleak.

Thanks for the stats Tim. Very interesting. This is a great example of why we have so many bases with 1 or 2 k's remaining; several on bases with CK>2000. There seems to frequently be those 1 or 2 k's that are very low weight in comparison to many of the others and so are extremely difficult to find the final prime for. R6 is one of the more glaring examples. 1 of its remaining 2 k's at n=1M is much lower weight than the other and was also significantly lower weight than any other of the 7 k's that remained at n=150K.

New S60 prime
 

S60 has another prime. 26 k's to go.

The prime is as follows, in top 10 listing:

2497 (88149)

Lower testing limit is n=87K and continuing. With a little luck, there might be another or 2 more primes, though statistically this recent prime should make the last prime, before n=125K.

Take care

KEP

S40 is complete to n=25K. 103 primes found, 455 k's remaining.
Here are the primes:
[CODE]88108*40^15093+1
490933*40^15397+1
434404*40^15402+1
584169*40^15420+1
174907*40^15478+1
200208*40^15498+1
507784*40^15501+1
149446*40^15582+1
498397*40^15616+1
261846*40^15690+1
127716*40^15894+1
519307*40^15910+1
659322*40^16100+1
212706*40^16115+1
237220*40^16212+1
468312*40^16269+1
465492*40^16306+1
723610*40^16340+1
326482*40^16695+1
740049*40^16713+1
72615*40^16854+1
771264*40^16901+1
691546*40^16911+1
436528*40^17166+1
184747*40^17228+1
584926*40^17229+1
39115*40^17282+1
687733*40^17303+1
357405*40^17432+1
514797*40^17444+1
669652*40^17489+1
189909*40^17491+1
815077*40^17518+1
118900*40^17769+1
528901*40^17802+1
357972*40^17968+1
30751*40^18004+1
800319*40^18085+1
9090*40^18122+1
637674*40^18210+1
415165*40^18225+1
466005*40^18301+1
570250*40^18303+1
131529*40^18380+1
659776*40^18388+1
732136*40^18463+1
362275*40^18507+1
140713*40^18620+1
187617*40^18768+1
748333*40^18834+1
784452*40^18993+1
575007*40^19004+1
527917*40^19140+1
275101*40^19213+1
390657*40^19232+1
631485*40^19313+1
158056*40^19440+1
347925*40^19619+1
730756*40^19707+1
113202*40^19734+1
350059*40^19856+1
673549*40^19870+1
91530*40^19888+1
491517*40^19936+1
324853*40^19949+1
142944*40^19996+1
543661*40^20068+1
148516*40^20104+1
646038*40^20338+1
535912*40^20492+1
761869*40^20526+1
644314*40^20633+1
422709*40^20647+1
595606*40^20919+1
337197*40^21248+1
328122*40^21479+1
739212*40^21511+1
15579*40^21573+1
436362*40^21627+1
136573*40^21769+1
154323*40^21775+1
743454*40^21834+1
230421*40^21924+1
821557*40^21999+1
485974*40^22094+1
340506*40^22128+1
576951*40^22161+1
277036*40^22293+1
536484*40^22427+1
720750*40^22443+1
591139*40^22512+1
82942*40^22801+1
474084*40^22974+1
458994*40^23153+1
191635*40^23696+1
56620*40^23859+1
263754*40^24150+1
546654*40^24174+1
766822*40^24187+1
47766*40^24214+1
748128*40^24390+1
598765*40^24586+1
785704*40^24983+1
[/CODE]Results, etc. have been e-mailed, as it is way too big to attach here.

Thanks for the great work on S40 Tim. It's nice to have it done. :smile:

Status update
 

R39 is to n=22.7K

18 primes found

Attached are the primes and the remaining k's